Subgroups — #504⋊C₉ #10588325

Order 576.

49 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#131⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×#504	C₃	1	1	yes	maximal, characteristic
3	#41⋊C₉	C₄	1	1	yes	characteristic
4	C₉×C₁₆	—	4	1	no	maximal
5	C₃×#131	C₂×C₃	1	1	yes	characteristic
6	C₃×M₃₂	—	3	1	no	—
7	C₂×C₃×C₁₆	—	3	1	no	—
8	Q₈⋊C₉	C₈	1	1	yes	characteristic
9	C₈×C₉	—	4	1	no	—
10	#504	C₉	1	1	yes	characteristic, complemented, Sylow
11	C₃×#41	C₃×C₄	1	1	yes	characteristic
12	C₃×M₁₆	—	3	1	no	—
13	C₂×C₃×C₈	—	3	1	no	—
14	C₃×C₁₆	—	3	1	no	—
15	C₃×C₁₆	A₄	1	1	yes	characteristic
16	C₄×C₉	—	4	1	no	—
17	#131	C₂×C₉	1	1	yes	characteristic
18	M₃₂	—	3	1	no	—
19	C₂×C₁₆	—	3	1	no	—
20	C₃×Q₈	C₃×C₈	1	1	yes	characteristic
21	C₃×D₄	—	3	1	no	—
22	C₂×C₃×C₄	—	3	1	no	—
23	C₃×C₈	—	3	1	no	—
24	C₃×C₈	C₂×A₄	1	1	yes	characteristic
25	C₂×C₉	—	4	1	no	—
26	#41	C₄×C₉	1	1	yes	characteristic
27	M₁₆	—	3	1	no	—
28	C₂×C₈	—	3	1	no	—
29	C₁₆	—	3	1	no	—
30	C₁₆	C₂²⋊C₉	1	1	yes	characteristic
31	C₂²×C₃	—	3	1	no	—
32	C₃×C₄	—	3	1	no	—
33	C₃×C₄	C₄×A₄	1	1	yes	characteristic
34	C₉	—	4	1	no	Sylow
35	Q₈	C₈×C₉	1	1	yes	characteristic
36	D₄	—	3	1	no	—
37	C₂×C₄	—	3	1	no	—
38	C₈	—	3	1	no	—
39	C₈	C₂×C₂²⋊C₉	1	1	yes	characteristic
40	C₂×C₃	—	6	1	no	—
41	C₂×C₃	C₈×A₄	1	1	yes	characteristic
42	C₂²	—	3	1	no	—
43	C₄	—	3	1	no	—
44	C₄	C₄×C₂²⋊C₉	1	1	yes	characteristic
45	C₃	#504⋊C₃	1	1	yes	characteristic
46	C₂	—	6	1	no	—
47	C₂	C₈×C₂²⋊C₉	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
10. #504	C₉	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.